4­13­16 Geo M2L16 Within and Between Figure Ratios.notebook
April 13, 2016
QUIZ TOMORROW 4/14/16
Date:
Lesson 16: Between­Figure and Within­Figure Ratios
1
4­13­16 Geo M2L16 Within and Between Figure Ratios.notebook
April 13, 2016
Example 1
b. Determine the height of the building using what you know about scale factors.
c. Determine the height of the building using ratios between similar figures.
d. Determine the height of the building using ratios within similar figures.
Example 3
The following right triangles are similar. We will determine the unknown side lengths by using ratios within the first triangle. For each of the triangles below we define the base as the horizontal length of the triangle and the height as the vertical length
a. Write and find the value of the ratio that compares the height to the hypotenuse of the leftmost triangle.
b. Write and find the value of the ratio that compares the base to the hypotenuse of the leftmost triangle.
c. Write and find the value of the ratio that compares the height to the base of the leftmost triangle.
2
4­13­16 Geo M2L16 Within and Between Figure Ratios.notebook
April 13, 2016
d. Use the triangle with lengths 3­4­5 and triangle A to answer the following questions.
i. Which ratio can be used to determine the height of triangle A ? ii. Which ratio can be used to determine the hypotenuse of triangle A? iii. Find the unknown lengths of triangle A.
e. Use the triangle with lengths 3­4­5 and triangle B to answer the following questions.
i. Which ratio can be used to determine the base of triangle B? ii. Which ratio can be used to determine the hypotenuse of triangle B? iii. Find the unknown lengths of Triangle B. 3
4­13­16 Geo M2L16 Within and Between Figure Ratios.notebook
April 13, 2016
Use the triangle with lengths 3­4­5 and triangle C to answer the following questions.
f.
i.
Which ratio can be used to determine the height of triangle C? ii. Which ratio can be used to determine the base of triangle C? iii. Find the unknown lengths of triangle C.
Example 4
Brian is photographing the Washington Monument and wonders how tall the monument is. Brian places his camera tripod approximately 100yds.from the base of the monument. Lying on the ground, he visually aligns the top of his tripod with the top of the monument and marks his location on the ground approximately 2ft 9in from the center of his tripod. Use Brian’s measurements to approximate the height of the Washington Monument. 4
4­13­16 Geo M2L16 Within and Between Figure Ratios.notebook
April 13, 2016
Lesson Summary
Do Now:
Quiz
REVIEW
Matteo is 6.2 feet tall. He is standing at the top of a
64 foot cliff. He dropped his new pretty pink cell phone
from the cliff and it floated out to sea. As Matteo stood
back 8 feet from the cliff his line of sight was even with
the pink cell phone in the sea. How far from the base of
the cliff was the cell phone when Matteo spotted it?
Round the answer to the nearest foot.
Begin with a Let x = statement and end with a therefore
statement.
5
4­13­16 Geo M2L16 Within and Between Figure Ratios.notebook
April 13, 2016
Lesson 16
Problem Set 6
4­13­16 Geo M2L16 Within and Between Figure Ratios.notebook
April 13, 2016
3. Catarina’s boat has come untied and floated away on the lake. She is standing atop a cliff that is 35 feet above the water in a lake. If she stands 10 feet from the edge of the cliff, she can visually align the top of the cliff with the water at the back of her boat. He eye level is 5.5 feet above the ground. Approximately how far out from the cliff is Catarina’s boat? 7